Question

вычислить производную сложной функции.

у=√sin(2x²-π)

                 ͞8

Answer 1

1/2*cos(x^2-П/8)*4x/sqrt(sin(2x^2-П/2))

Answer 2

$y'=(sqrt {sin {frac {2x^2-pi}{8}}})'= frac{(sin {frac {2x^2-pi}{8}})'} {2sqrt {sin {frac {2x^2-pi}{8}}}}= frac {cos {frac {2x^2-pi}{8}}} {2sqrt {sin {frac {2x^2-pi}{8}}}} *(frac {2x^2-pi}{8})'}=$

$=frac {cos {frac {2x^2-pi}{8}}} {2sqrt {sin {frac {2x^2-pi}{8}}}} *(frac {1}{8})}*(2x^2-pi)'= =frac {cos {frac {2x^2-pi}{8}}} {2sqrt {sin {frac {2x^2-pi}{8}}}} *(frac {1}{8})}*(4x-0)=$

$=frac {x cos {frac {2x^2-pi}{8}}} {4sqrt {sin {frac {2x^2-pi}{8}}}}$